Final answer:
The Texan commissioners' responsibility did not include convincing the US that they wanted to become a state, as many Texans did desire annexation but faced political hesitancy from American politicians.
Step-by-step explanation:
The responsibilities of the Texan commissioners who went to the United States after the consultation did not include 'convincing the US that they wanted to become a state.' This options is incorrect because, as documented in the Lone Star Republic's history, many Texans, including influential figures like Sam Houston and William B. Travis, hoped for Texas to become a part of the United States.
However, American politicians were hesitant to annex Texas due to concerns over instigating war with Mexico and reigniting the contentious issue of slavery. Despite many Texans desiring the annexation, the official stance of the Texan commissioners at the time was not to promote statehood, but rather to secure recognition, aid, and protection as an independent nation.